Related papers: A Cutoff Phenomenon for Quantum Markov Chains
The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…
In this article we study the so-called cut-off phenomenon in the total variation distance when $n\to \infty$ for the family of continuous-time stochastic processes indexed by $n\in \mathbb{N}$, \[ \left( \mathcal{Z}^{(n)}_t=…
We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white…
We resolve the long-standing problem of elucidating the cutoff phenomenon for a vast and important class of Markov processes, namely Markov diffusions with non-negative Bakry-\'Emery curvature. More precisely, we prove that any sequence of…
In this paper we present, in the context of Diaconis' paradigm, a general method to detect the cutoff phenomenon. We use this method to prove cutoff in a variety of models, some already known and others not yet appeared in literature,…
The cutoff phenomenon describes a sharp transition in the convergence of an ergodic finite Markov chain to equilibrium. Of particular interest is understanding this convergence for the simple random walk on a bounded-degree expander graph.…
The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…
In the present paper, we consider a class of Markov processes on the discrete circle which has been introduced by K\"onig, O'Connell and Roch. These processes describe movements of exchangeable interacting particles and are discrete…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…
We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing…
We find Gaussian cutoff profiles for the total variation distance to stationarity of a random walk on a multiplex network: a finite number of directed configuration models sharing a vertex set, each with its own bounded degree distribution…
In this paper, we study the cut-off phenomenon under the total variation distance of $d$-dimensional Ornstein-Uhlenbeck processes which are driven by L\'evy processes. That is to say, under the total variation distance, there is an abrupt…
A finite ergodic Markov chain exhibits cutoff if its distance to equilibrium remains close to its initial value over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Originally discovered in the…
The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the $d$-dimensional torus $(Z/nZ)^d$…
We analyze the convergence rates for a family of auto-regressive Markov chains $(X^{(n)}_k)_{k\geq 0}$ on $\mathbb R^d$, where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The…
The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. In 1996, Diaconis surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite…
We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing…
Establishing cutoff, an abrupt transition from "not mixed" to "well mixed", is a classical topic in the theory of mixing times for Markov chains. Interest has grown recently in determining not only the existence of cutoff and the order of…
We consider an analogue of the Kac random walk on the special orthogonal group $SO(N)$, in which at each step a random rotation is performed in a randomly chosen 2-plane of $\bR^N$. We obtain sharp asymptotics for the rate of convergence in…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…